Hodge numbers attached to a polynomial map

Details Hodge numbers attached to a polynomial map Hodge numbers attached to a polynomial map

1997-01-08

arxiv.org/abs/alg-geom/9701003v1

Mathematics

Algebraic Geometry

AMS-LaTeX, 33 pages

Scientific paper

Given a polynomial map $f:\Bbb C^{n+1}\to\Bbb C$, one can attach to it a geometrical variation of mixed Hodge structures (MHS) which gives rise to a limit MHS. The equivariant Hodge numbers of this MHS are analytical invariants of the polynomial map and reflect its asymptotic behaviour. In this paper we compute them for a class of generic polynomials, in terms of Hodge numbers attached to isolated hypersurface singularities and Hodge numbers of cyclic coverings of projective space branched along a hypersurface.

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